Lemma 26.7.5. Let $(X, \mathcal{O}_ X) = (\mathop{\mathrm{Spec}}(R), \mathcal{O}_{\mathop{\mathrm{Spec}}(R)})$ be an affine scheme. The functors $M \mapsto \widetilde M$ and $\mathcal{F} \mapsto \Gamma (X, \mathcal{F})$ define quasi-inverse equivalences of categories

$\xymatrix{ \mathit{QCoh}(\mathcal{O}_ X) \ar@<1ex>[r] & \text{Mod}_ R \ar@<1ex>[l] }$

between the category of quasi-coherent $\mathcal{O}_ X$-modules and the category of $R$-modules.

Comment #427 by Jeroen Zuiddam on

I am getting a parse error in the display.

Comment #428 by on

OK, I think this is due to an XyJax parsing error. I'll investigate more. Thanks for the report!

There are also:

• 5 comment(s) on Section 26.7: Quasi-coherent sheaves on affines

In your comment you can use Markdown and LaTeX style mathematics (enclose it like $\pi$). A preview option is available if you wish to see how it works out (just click on the eye in the toolbar).